Question

In the following circuit p-n-junction diodes $D_1,D_2$ and $D_3$ are ideal for the following potential of $A$ and $B$, the correct increasing order of resistance between $A$ and $B$ will be -

$\left(i\right)-10\text{V},-5\text{V}\left(ii\right)-5\text{V},-10\text{V}\left(iii\right)-4\text{V},-12\text{V}$

• A. $\left(i\right)<\left(ii\right)<\left(iii\right)$
• B. $\left(iii\right)<\left(ii\right)<\left(i\right)$
• C. $\left(ii\right)=\left(iii\right)<\left(i\right)$
• D. $\left(i\right)=\left(iii\right)<\left(ii\right)$

Answer 1

The correct option is C $\left(ii\right)=\left(iii\right)<\left(i\right)$

$\left(i\right)V_A=-10\text{V},V_B=-5\text{V}$
$\to D_1,D_3\to R.B$
$\Rightarrow$ open
and $D_2\to F.B$
$\Rightarrow short$
$\Rightarrow R_{AB\left(i\right)}=\frac{R}{4}+R+\frac{R}{4}$
$=R+\frac{R}{2}=\frac{3R}{2}$
$\left(ii\right)V_A=-5\text{V},V_B=-10\text{V}$
$\Rightarrow D_1,D_3\to FB$
$D_2\to RB$
$R_{AB\left(ii\right)}=\frac{R}{4}+\frac{R}{2}+\frac{R}{4}=R$
$\left(iii\right)V_A=-4\text{V},V_B=-12\text{V}$
$\Rightarrow D_1,D_3\to FB$
$D_2\to RB.$
$R_{AB\left(iii\right)}=\frac{R}{4}+\frac{R}{2}+\frac{R}{4}=R$
$\Rightarrow \left(ii\right)=\left(iii\right)<\left(i\right)$